The general form of a hyperbola is 9x2−5y2−54x−10y+31=0. What is the standard form of this hyperbola?

The standard form of this hyperbola is .

Step-by-step explanation:

From Analytical Geometry, the standard form of the hyperbola is defined by the following expression:

(1)

Where:

- Independent variable, dimensionless.

- Dependent variable, dimensionless.

- Semiaxis lengths, dimensionless.

- Coordinates of the center, dimensionless.

Let the hyperbola be defined by , we proceed to derive the standard form by algebraic means:

1)   Given

2) Commutative and associative properties/

3) Modulative, distributive and associative properties//Existence of the additive inverse

4) Perfect trinomial square//Commutative property

5) Distributive property//Definition of addition and subtraction.

6)    /Compatibility with addition/Existence of additive inverse/Modulative property.

7)   Compatibility with multiplication/Definition of division/Distributive property/Result.

The standard form of this hyperbola is .

the one on the bottom left

step-by-step explanation:

all of the other ones have a specific pattern